北京长富宫酒店:tan(x+y)=0.4,tan(y-45°)=0.25,则tan(x+45°)=?要过程
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因为(x+y)-(y-45°)=x+45°
所以tan[(x+y)-(y-45°)]=tan(x+45°)
左边展开:
tan(x+45°)
=[tan(x+y)-tan(y-45°)]/[1+tan(x+y)*tan(y-45°)]
=(0.4-0.25)/(1+0.4*0.25)
=3/22
tan(x+y)=tanx+tany/(1-tanxtany)=0.4
由此可得tany=5/3 tanx=(不算了) 再由公式得结果
tan(x+45°)=tan[(x+y)-(y-45°)]
=[tan(x+y)-tan(y-45°)]/[1+tan(x+y)*tan(y-45°)]
=(0.4-0.25)/(1+0.4*0.25)
=0.15/1.1
=3/22
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